The Kremlin response comes after U.S. and Russian military officials held a video conference to discuss Thursday's strikes.
"The object which had suffered bombardment was located more than 300 km far from borders of territories claimed by the American party as ones controlled by the opposition joined the ceasefire regime," the Russian Defense Ministry said in the statement.
And Russian forces "forewarned member states of the U.S.-led coalition about the ground targets to strike on," the statement added.
In recent months, the Russian Defense Ministry has suggested "compiling a joint map with actual information about location of forces active in Syria," according to the statement. "However, there has been no significant progress reached."
U.S. and Russia talks
The video conference addressing the Russian airstrikes was convened under the auspices of the Safety of Flight Memorandum of Understanding, an arrangement between the counter-ISIL coalition and Russian Federation to maintain safety in the air space over Syria.
The discussion was unusual, because that communications channel was not established for such a purpose.
"Department officials expressed strong concerns about the attack on the coalition-supported counter-ISIL forces at the At-Tanf garrison, which included forces that are participants in the cessation of hostilities in Syria, and emphasized that those concerns would be addressed through ongoing diplomatic discussions on the cessation of hostilities," Pentagon press secretary Peter Cook said Saturday.
"Regarding safety, department officials conveyed that Russia's continued strikes at At-Tanf, even after U.S. attempts to inform Russian forces through proper channels of on-going coalition air support to the counter-ISIL forces, created safety concerns for U.S. and coalition forces," Cook added.
The strikes, which the U.S. says killed some New Syrian Army troops, occurred about six miles from the Jordanian border, according to a U.S. defense official. The U.S. diverted armed FA-18s to the area after the first round of two strikes, and the pilots then tried to call the Russians on a previously agreed-upon pilot-to-pilot communications channel but did not receive an answer.
As soon as the U.S. jets left the area to refuel, the Russians came back for another round of bombing, the defense official said.
"Russian aircraft conducted a series of airstrikes near al-Tanf against Syrian counter-ISIL forces that included individuals who have received U.S. support. Russian aircraft have not been active in this area of Southern Syria for some time, and there were no Syrian regime or Russian ground forces in the vicinity," a senior defense official said. "Russia's latest actions raise serious concern about Russian intentions. We will seek an explanation from Russia on why it took this action and assurances this will not happen again."
The first two bombing runs by the Russians were carried out by two SU-24 Russian jets coming out of their base near Latakia. The jets dropped what is believed to be the equivalent of U.S. 500-pound bombs and possibly cluster munitions, according to the U.S. defense official.
Eye in the sky
U.S. officials are watching the situation closely. Asked about the strikes Friday, Defense Secretary Ash Carter said it raised questions about whether the Russians were actually in Syria to fight Islamic extremists.
"Here's a case where they actually attacked forces that were fighting ISIL. And if that was their intention, that's the opposite of what they said they were going to do," Carter said. "If not, then it says something about the quality of the information upon which they make airstrikes."
U.S. and Russian forces in Syria have had tense relations since the country devolved into civil war. The U.S. has backed rebel groups while the Russians have supported Syrian president Bashar al-Assad.